Continuation of solutions of constrained extremum problems and nonlinear eigenvalue problems

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Groesen, E.W.C. van (1980) Continuation of solutions of constrained extremum problems and nonlinear eigenvalue problems. Mathematical Modelling, 1 (3). pp. 255-270. ISSN 0270-0255

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Abstract:In this paper we continue our investigations, begun in the previous paper, of describing the solution sets of a constrained extremum problems inf f(u),
uεt−1(p) (*) where f and t are twice continuously differentiable functionals on a reflexive Banach space V, and t-1(p) denotes the level set of the functional t with value p ε R.
Considering p as a parameter in (*) we obtain results concerning the continuation of solutions of (*) and consequently also concerning specific solution branches of the nonlinear eigenvalue problem f′(u) = μt′(u) (**). The general results are applied to functionals which lead to nonlinear eigenvalue problems of a semilinear elliiptic type and in particular we cosider a specific example for which there occurs “bending” of a solution curve (u,μ) of (**).
Item Type:Article
Copyright:© 1980 Elsevier Science B.V.
Link to this item:http://purl.utwente.nl/publications/56155
Official URL:http://dx.doi.org/10.1016/0270-0255(80)90061-5
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